# Math Table

## Welcome!

Math Table is a seminar jointly run by the Harvard Mathematics department and undergraduate students. The purpose of Math Table is to provide an opportunity for undergraduates to be exposed to interesting mathematical topics, as well as to gain experience in communicating and teaching mathematics.

Talks take place in **Science Center 507** every **Tuesday** at **6:00 PM**. Talks are **catered**, with different kinds of food every week. We do our best to accommodate all dietary needs, so if you have any concerns please send us an email in advance (see "About" tab for contacts).

### Who can attend/give talks?

* All* Harvard undergraduate students are welcome to attend

*Math Table talk and to sign up to give a talk. Talks come in a wide array of topics, background levels, and styles (see the "Resources" tab). The Math Table organizers (see "About" tab) are here to help you pick topics and develop your talk, so even if you aren't sure about what your topic is, you should come speak with us!*

**any**To **sign up** to give a talk, or if you have any **questions** about Math Table, please send an email to spaul@math.harvard.edu and/or dzemke@g.harvard.edu, or to any of our undergraduate coordinators (see "About" tab for contacts).

## Upcoming Talks

### Games in New Contexts

**Speaker: **Kelsey Houston-Edwards (Olin College)

**Abstract: **We'll play some familiar games in some unfamiliar contexts and try to generate conjectures about the possible outcomes. Then we'll prove some of these conjectures using theorems from combinatorics and game theory. This exploration should be accessible to all, with options to dive deeper into the proofs or just play some games.

### Tuesday, November 13 (6:00pm, SC 507)

### Tuesday, November 6 (6:00pm, SC 507)

### Why Five Platonic Solids? (It's not as simple as you think!)

**Speaker: **Glen Whitney

**Abstract: **There are various things in math that you just know are true: among all shapes with a given surface area, the sphere encloses the most volume, a trefoil knot is really knotted, a continuous simple closed curve has an inside and an outside, etc. Yet when you try to prove them, you suddenly discover that you are sticking your toes into deep (and possibly shark-infested) waters. At this math table, I'll try to convince you that the familiar fact that there are just five regular solids is a fact of this particularly vexing character (and hopefully have a bit of fun along the way).

## Recent Talks

### Divide and Conquer and 1-Center Clustering

**Speaker: **Shyam Narayanan

**Abstract: **Divide and Conquer is a common technique in theoretical computer science and has many cool applications! I'll begin by talking briefly about algorithms and the divide and conquer technique, and will explain how this technique can be used for the well-known Merge Sort algorithm. I'll finally explain the 1-Center Clustering with Outliers problem and show how one can get a linear-time algorithm for it using divide and conquer techniques.

### Tuesday, October 30 (6:00pm, SC 507)

### Tuesday, October 23 (6:00pm, SC 507)

### The Goldbach Comet

**Speaker: **Oliver Knill

**Abstract: **

The Goldbach comet is the graph of the function which tells in how many ways an integer 2n can be written as a sum of two primes. While it is preposterous trying to prove that the function is positive (this is the Goldbach conjecture), one can investigate the comet statistically and experiment in other number systems. I'm personally convinced that EVERY mathematician has secretly worked on the problem, but of course few admit it as there is a serious danger to reach a high score on the ``Prime numbers crackpot index" of Chris Caldwell (https://primes.utm.edu/notes/crackpot.html) Having not much to lose in matters of reputation, I can tell about my own foolish attempts which started 35 years ago both trying to find a root of the comet as well as trying to prove that none exists. There will be also a bit of history. While serious mathematicians use heavy analytic number theory, I will explain a simple real analysis attempt which only uses single variable calculus and relates to the Riemann zeta function. There is no reason for excitement: the approach does not prove it but there are interesting patterns and opportunities to experiment with computer algebra systems.

### Playing the St. Petersburg Paradox

**Speaker: **Mark Kong

**Abstract: **The Strong Law of Large Numbers is a way to formalize the notion that "Expected value is what you expect to get on average in the long run." We will discuss an analog of this claim for the St. Petersburg Paradox, a game with infinite expected value. Time permitting, we will also mention an analog of the Weak Law of Large Numbers.

### Tuesday, October 16 (6:00pm, SC 507)

### Tuesday, October 9 (6:00pm, SC 507)

### Graduate School Panel

A panel of graduate students will host a question and answer session on applying for and attending graduate school. Undergraduates will have the opportunity to ask questions, and learn more about what graduate work entails.

Panelists TBA

### Tuesday, October 2 (6:00pm, SC 507)

### Eliminating Aperiodicity in Tilings

**Speaker: **Daniel Kim

**Abstract: **Given a set of tiles, can you use them to cover the entire plane without any overlaps? The attempt to answer this question led to the discovery of various tilings exhibiting intricate structures, such as the Wang tilings, the Penrose tilings, and the Socolar–Taylor tiling. In this talk, I will try to eliminate these beautiful tilings and make everything periodic and orderly.

### Tuesday, Sep 25 (6:00pm, SC 507)

### Math Experience Round Table, Hosted by CREWS

Come on by to share and learn what Harvard students have done with math outside their classes, such as REUs, internships, and other research. Dinner at 6:00, panel starts at 6:20. Sponsored by CREWS (Clusters Engaging Womxn in Mathematics).

The idea is to have students share (five minutes) the who, what, when, and where of a mathematical experience that was outside of their Harvard coursework. It would be great to highlight a variety of experiences ranging from intensive semesters abroad to seminars attended at MIT to internships to REUs or other work. It will be helpful for other students to hear how people found out about these experiences and the nuts and bolts of what was involved in participating!

### Tuesday, Sep 18 (5:30pm, SC 232)

**Speaker: **Sebastian Vasey

**Title: **Hypercomputation

**Abstract: **David Hilbert's "Entscheidungsproblem" asks for an algorithm to prove or disprove any mathematical statement. The non-existence of such an algorithm was proven independently by Church and Turing. This is often interpreted as meaning that there is no streamlined method to prove something: it takes hard work and creativity... Or does it? What did Church and Turing precisely prove? Could we imagine a hypercomputer capable of performing infinitely-many steps in a finite time? Could we build such a machine, or at least come close? I will discuss these questions and more.

### Tuesday, Sep 11 (5:30pm, SC 232)

**Speaker: **Davis Lazowski

**Title: **Quiver Representations

**Abstract: **Quiver representations give a beautiful, pictorial way to encode algebraic data. In this talk, the speaker will introduce quiver representations and study simple examples. At the end, the speaker will briefly survey applications to Lie theory and algebraic topology. The talk assumes some knowledge of linear algebra.

### Tuesday, Sep 4 (5:30pm, SC 232)

**Speaker: **Cliff Taubes

**Title: **Mysteries of 4 Dimensions

**Abstract: **The classification of spaces of dimensions 1-3 and 5—∞ is well understood. Dimension 4 is not understood. In fact, there are no compelling conjectures as to what the answer should be. I hope to explain some of this in the talk.

**At 5:00pm in the same room, Gabriel Goldberg will be giving an overview of his fall tutorial "Infinite Combinatorics".**